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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_39.8', 'a10': [-1.0, -1.4081532572346456e-30], 'a2': [2.9010907910729803e-30, -1.0], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [2.9010907910729803e-30, -1.0], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [2.9010907910729803e-30, -1.0], 'a8': [-7.040766286173228e-31, 1.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.18111523857559697, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '39.8', 'coeff_info': ['x^4 - 1', '6.12323399573677e-17 + 1.00000000000000*I', '\\\\zeta_{4}'], 'conductor': 39, 'conductor_radical': 39, 'conjugate': 'dirichlet_L_39.5', 'degree': 1, 'dirichlet_coefficients': [1, '-I', 0, -1, '-I', 0, '-I', 'I', 0, -1, 'I', 0, 0, -1, 0, 1, 1, 0, 'I', 'I', 0, 1, 1, 0, -1, 0, 0, 'I', -1, 0, 'I', '-I', 0, '-I', -1, 0, '-I', 1, 0, 1, '-I', 0, -1, '-I', 0, '-I', 'I', 0, -1, 'I', 0, 0, -1, 0, 1, 1, 0, 'I', 'I', 0, 1, 1, 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'193.46233218484464040020680596894', '193.76307052858178327170885695599', '195.14481483397087650805379073879', '195.60914548924851997389355419943', '196.62993356919884721473406226288', '197.89967838534119921580955486297', '198.75415873134604685923250095464', '199.704344141315630056839236818384'], 'prelabel': '1-39-39.8-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.18111523857559697, 'root_angle': -0.5935835209054995, 'root_number': '-0.289784148688430089716825558519-0.957092026489052849592220722565*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.296791760453', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(4)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.712276872889636034014832491054-0.551057479064483683981908440859*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.44644689777', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.80425591722', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.12441979962', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.18111523857559697, 'bad_primes': [3, 13], 'central_character': '39.8', 'conductor': 39, 'conductor_radical': 39, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/39/8'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-39-39.8-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-39-39.8-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.18111523857559697, 'root_angle': -0.29679176045274974, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44644689777', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_39.8', 'Lhash_array': ['dirichlet_L_39.8'], 'label': '1-39-39.8-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/39/8'}